Measurement of the Full Shape of the Thermal Sunyaev-Zeldovich Power Spectrum from South Pole Telescope and {\it Herschel}-SPIRE Observations

TL;DR

The paper presents a measurement of the full shape of the thermal Sunyaev-Zeldovich power spectrum over multipoles 500–5000 by combining SPTpol, SPT-3G, and Herschel-SPIRE data to construct Compton-y maps via harmonic-space linear combination. The authors generate multiple map bundles (MV, CMB-free, CIB-min, Radio-min) and use Agora simulations to derive cross-spectra while mitigating foregrounds, achieving a 9.3σ tSZ detection and demonstrating consistency with Planck, ACT, and SPT-3G results. They reconstruct the scale-dependent tSZ×CIB cross-correlation, finding evidence for a nonzero correlation on large scales that diminishes at high ell, and study how cluster and radio source masking affect the tSZ power spectrum. The work yields the deepest tSZ maps to date, provides new constraints on intracluster medium physics and baryonic feedback, and makes the tSZ maps and bandpowers publicly available for broader cosmological and astrophysical analyses.

Abstract

We present a measurement of the full shape of the power spectrum of the thermal Sunyaev-Zeldovich (tSZ) effect down to arcminute scales using cosmic microwave background (CMB) data from the South Pole Telescope (SPT) over roughly 100 ${\rm deg}^{2}$ field. The analysis incorporates data from the 2019/20 seasons of the SPT-3G survey in bands centered at 95, 150, and 220 GHz; from the full SPTpol dataset at 150 GHz; and from {\it Herschel}-SPIRE survey in bands centered at 600 and 857 GHz. We combine data from all the above bands using linear combination (LC) techniques to produce a tSZ or Compton-$y$ map. We modify the LC weights to produce multiple versions of the Compton-$y$ map, including minimum-variance (MV) and foreground-minimized (-min) maps. We measure the auto- and cross-spectra of a subset of these maps in the range $\ell \in [500, 5000]$. While this power spectrum includes contributions from signals other than tSZ, we present numerous checks to show that the most challenging foreground signal, the cosmic infrared background (CIB) is much lower than the desired tSZ signal in the scales of interest in this work. The final tSZ power spectrum is measured at $9.3σ$ with both the MV and CIB-min maps. Our results are consistent with those reported in other CMB surveys across the literature. Using the difference in the tSZ power spectrum from MV and CIB-min maps, we reconstruct the scale-dependent tSZ-CIB cross-correlation $ρ_{\ell}^{\rm tSZ \times CIB}$, finding $3.1σ$ evidence for a nonzero correlation coefficient that is positive on large scales and approaches zero for $\ell > 2500$. This result represents the deepest tSZ maps ever produced and provides new constraints that can help refine astrophysical feedback mechanisms and models of the intracluster medium.

Figures (10)

• Figure 1: Azimuthally averaged LC weights for the MV and the CIB-min Compton-$y$ maps. The solid (dashed) curves correspond to MV (CIB-min) maps. Since the weights are much smaller for the Herschel-SPIRE 600 (857) bands compared to the other bands, they have been multiplied by $\times 100$ ($\times 1000$) for clarity in this plot. As mentioned in the text, for the ease of analysis, we assume same weights for the 150 GHz channel from both SPT-3G and SPTpol.
• Figure 2: MV Compton-$y$ map created using the full dataset. The increments (red dots) correspond to the cluster locations and the negative bowls around them correspond to the scan-direction filtering of the SPT maps, which we correct using TF during the power spectrum estimation stage. The inset panel in the top right shows the $6^{\prime} \times 6^{\prime}$ stack of clusters with $S/N \ge 20$ from kornoelje25.
• Figure 3: The total measured power spectra from data are shown as open circles in top panels for MV (left), CIB-min (middle), and the cross-spectrum between the two (right). The dash-dotted line corresponds to the expectation spectra of the undesired components with the individual contributions shown in different colors: CMB in yellow, CIB in red, kSZ in green and radio in blue. The dash‑dotted curve does not have the tSZ contribution, so it is not expected to align with the data points. The bands correspond to the systematic scatter in each component (see text in §\ref{['sec_sys_errors']} for details). The error budgets (black) are presented in the bottom panels and have been decomposed into statistical (gray) and systematic errors from the undesired signals and calibration uncertainties (all other colors).
• Figure 4: The tSZ power spectra measured at $9.3\sigma$ using the CIB-min maps is shown in green. The error bars include contributions from both statistical and systematic errors, and have significant off-diagonal correlations due to the non-Gaussian nature of the signals. We also show the results from Planck (PR4) as yellow hexagons; ACT (DR6) as a teal octagon; SPT-3G (D1) as blue squares; and a joint analysis of ACT, Planck, and SPT as red diamonds. While the results in this work are slightly higher than ACT at $\ell = 3000$ by $1\sigma$, we find excellent agreement with Planck in the overlapping scales and also with the results from SPT-3G and efstathiou25 over a wide range of scales. For reference, we also show the power spectra from versions of the FLAMINGO simulations as gray curves: the dotted curve is for the low $S_{8}$ (LS8) while the dashed curve corresponds to the model with low $S_{8}$ and with high ($f_{\rm gas} - 8\sigma$) AGN feedback.
• Figure 5: Reconstructed tSZ power spectra measured from data (left) and simulations (right): MV (red squares), CIB-min (green circles), and their cross-spectrum (yellow diamonds). Left panel: In data, the tSZ power spectrum is measured at $\sim 9.3\sigma$ in all the three cases. At $\ell \gtrsim 2500$, we find excellent agreement between all three spectra. The differences at lower multipoles are due to the different levels of tSZ $\times$ CIB, which results in a partial cancellation of the recovered tSZ signal. Right panels: The input tSZ power spectrum in simulations is show as the gray curve. The top right panel corresponds to Agora simulations with all the components but after explicitly removing the tSZ $\times$ CIB using (CMB + kSZ + tSZ + Uncorr-CIB + Uncorr-radio). In the absence of tSZ $\times$ CIB, all of the estimators return unbiased results. The bottom right panel contains tSZ $\times$ CIB, and in this case, we find the MV estimate to be biased low at large scales. The CIB-min remains unbiased and MV $\times$ CIB-min lies in between the two. The simulations results are obtained after averaging over 25 realizations. This trend is similar between data and simulations, although unlike in the empirical data, the simulations show that MV remains biased even at small scales. This is due to the differences in tSZ $\times$ CIB between data and simulations. The bottom right panel is provided solely for illustration to build intuition about how the tSZ $\times$ CIB can bias the tSZ power spectrum, and we emphasize that we do not rely on tSZ $\times$ CIB in simulations for any part of our analysis.